Peel Elementary Teachers Local (PETL)

Saturday March 25th, 2017

Thanks for inviting me to learn with you on a Saturday in Peel! The group was energetic and excited to learn about meaningful manipulative use, counting principles, the progression of multiplication/division and the importance of concreteness fading!

Here’s a summary of what we explored today. Looking forward to connecting again soon!

After a brief presentation about avoiding the rush to the algorithm, we took some time to explore a 3 act math task with a very low-floor and high-ceiling, called the Airplane Problem:

How many seats are there?

From Subitizing and Unitizing to Multiplicative and Algebraic Thinking
This 3 act math task was designed specifically to have a very low floor in order to be useful from primary grades and a high ceiling with an opportunity for many extensions so the task can be used in junior and intermediate classrooms. While I believe this task can touch on many different specific expectations at man...

A Progression of Counting and Quantity
As a former secondary math teacher and intermediate math coach, my new role as K-12 math consultant has led to a wealth of knowledge that I wish I had during my years spent in the classroom. My conversations about student learning needs with intermediate and senior math teachers always seems to come down to gaps in student understanding, however rarely wer...

Arrays and Area Models to The Standard Algorithm
Did you know that the words "array" and "area model" appear in the Grade 1-8 Math Curriculum a combined 22 times?
Not only do arrays and area models help to support the development of proportional reasoning when we formally introduce multiplication in primary, but they also help us understand how to develop strategies that lead to building numbe...

Japanese Multiplication? Chinese Multiplication? Line Multiplication?
Whatever it's called, it's only a trick if you simply memorize without meaning
Have you ever wondered why Japanese multiplication works?
I've heard some call it Chinese multiplication, multiplication from India, Vedic multiplication, stick multiplication, line multiplication and many more.
While many might argue as to the...

3 Act Math Task: Donut Delight

After lunch, we explored the Donut Delight 3 act math task where we played with multiplication to predict how many donuts there were in the “double hundred dozen” box and then used repeated subtraction to lead to a flexible division algorithm for division when we tried to find how many layers there were.

How many doughnuts are there?

Sparking Curiosity to Promote Conceptual Understanding of Multiplication and Division
When one of our district math leads, Brennan Jones asked me to brainstorm some ways we could help his staff engage in some professional development around division and incorporate a 3 act math task into the learning, I immediately thought of some contexts where arrays, base ten blocks and area models cou...

Progression of Division

We spent some time working with the progression of division in most groups as well. Here are some screenshots of what we looked at:

Concreteness Fading

We attempted to summarize the use of manipulatives on a continuum called “Concreteness Fading”. While the name suggests that concrete manipulatives fade away over time, it is important to remember that they fade away with one layer of abstraction and then reappear as a new layer is “piled” on.

Hope you folks found this professional learning experience useful.

I’d be delighted to come back and learn alongside you all again sometime soon!

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About Kyle Pearce

Kyle Pearce is the K-12 Mathematics Consultant with the Greater Essex County District School Board, where he enjoys uncovering creative ways to spark curiosity through the inquiry process using tasks that are contextual, visual and concrete. He enjoys sharing his most recent learning in mathematics pedagogy and effective uses of technology by delivering workshops both near and far.